These machines were purchased by the office in one batch. So they have power supplies, motherboards and disks from the same batches. This pretty well confirms that the failure was internal.
New Netgear Wireless Modem Router
This was purchased to replace the old ADSL modem, which had its annoyances, particularly its inability to handle DHCP. (It has to be remembered that I am old enough to have been around when we didn't have DNS, much less DHCP, which appeared in the 1990s.) It includes a 4-point switch so it also replaces my switch. It only has four points instead of five, but one is no longer required by the wireless access point. So it replaces three different devices.
(Netgear is an American company but of course it's made in China like everything else. A cartoon in the paper showed a naked man in an empty room with the caption: "How's the boycott of Chinese goods going?")
First attempt to get it to run failed; it couldn't seem to handle Allison's settings. Second attempt was from Hillary (the laptop). This succeeded easily, allowing me to configure PPPoA and the wireless. Testing the wireless was as simple as unplugging to network cable. Then hooked up Allison, which then was able to connect to the internet, even without altering her settings to obtain an IP address automatically (ie DHCP) and to obtain a DNS server automatically. Switched the settings over and still worked. Powered up Sandy, who sulked about her IP address being allocated to another machine. Brought up the Apple TCP/IP control panel and selected "use DHCP server". Everything then worked.